DEGREE PROJECT IN MECHANICAL ENGINEERING, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2019 Robust motion control strategies for hydrofoil-equipped naval vessels considering scaling effects HENRIK STRÖMQVIST KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF INDUSTRIAL ENGINEERING AND MANAGEMENT Examensarbete MMK 2019:399 Robusta rörelsestyrningsstrategier för bärplansutrustade vattenfarkoster rörande skalningseffekter Henrik Strömqvist Godkänt Examinator Handledare 2019-06-24 Lei Feng Binbin Lian Uppdragsgivare Kontaktperson Maritime Robotics Lab, KTH Ivan Stenius Sammanfattning Bärplansutrustade fartyg är inte något som är särskilt nytt. Tekniken går så långt tillbaka som början av 1900-talet och nya framsteg görs inom området. Huvudprincipen för bärplan är att använda flödesdynamik för att generera lyftkraft likt ett flygplan och lyfta fartygets skrov ur vattnet, vilket i sin tur minskar motståndet när farkosten förflyttar sig. På KTH har en ny typ av båt konstruerats som bygger på denna princip kallad FoilCart. Dess konstruktion gör att dess rörelsestyrning påminner om en inverterad pendel vilket är ett klassiskt kontrollproblem vilket kan lösas på många olika sätt. Tidigare studier har inriktat sig på rörelse runt lutningsaxeln, men FoilCart-prototypen innefattar även rörelse kring rullningsaxeln. Beteendet hos denna inverterade pendel är därför också mer komplext genom att vara i flera frihetsgrader, roterande och translaterande runt flera axlar. Tanken är att bedöma vilken inverkan detta har på övergripande robusthet och stabilitet genom att studera möjliga kopplingseffekter mellan rullning och lutning. Avhandlingen syftar också till att studera möjliga skalningseffekter när prototypens fysiska parametrar ändras. Detta görs som en viktig bedömning av farkosten som en autonom drönare, eftersom den kanske kan användas för kartläggning av havsdjup där energieffektivitet är mycket väsentlig. Flera kontrollalgoritmer utvärderas så som klassiska PID och linjära kvadratiska metoder. Dessa används och testas genom simulering i Simscape Multibody som ett sätt att verifiera funktion. Ytterligare strategier för rörelsestyrning utvecklas även för att öka stabiliteten och robustheten genom att t ex öka mängden kontrollerbara variabler. Resultaten visar att kopplingseffekterna är minimala när systemet utsätts för störningar och pekar på att den förenklade reglerkonstruktionen är möjlig, men detta kan bara konstateras när rörelsen sker kring jämviktspunkten eftersom en linjärisering görs. När det gäller skalningseffekter behöver farkosten ett snabbare svar från kontrollern som i sin tur ställer högre krav på hårdvaran när farkosten skalas ner. Till exempel med relativt långsamma servos för att styra systemet uppstår ett oscillerande beteende. Ökad frekvens i reglerslingan innebär också en ökad förstärkning av högfrekvent brus vilket kan leda till oönskat beteende. Master of Science Thesis MMK 2019:399 Robust motion control strategies for hydrofoil-equipped naval vessels considering scaling effects Henrik Strömqvist Approved Examiner Supervisor 2019-06-24 Lei Feng Binbin Lian Commissioner Contact person Maritime Robotics Lab, KTH Ivan Stenius Abstract Hydrofoil-equipped naval vessels are not new. The technique appeared at the beginning of the 20th century and there are still new developments within the field. The main principle of hydrofoils is to use fluid dynamics to generate lift much like an aircraft and lift the hull of the craft out of the water, thus reducing drag while traversing the water surface. At KTH, Royal Institute of Technology a new craft called FoilCart has been built using this principle. Due to the design, the motion control resembles that of an inverted pendulum which is a classical control problem with many ways of reaching stable behavior. Previous studies have focused on pitch actuation, however the FoilCart incorporates roll actuation through hydrofoils as well which opens up new possibilities on movement. The nature of this inverted pendulum is therefore also made more complex by being in several degrees of freedom, rotating and translating around multiple axes. The idea is to assess the impact this has on overall robustness and stability by studying possible coupling effects between roll and pitch. The thesis also aims to study possible scaling effects when the physical parameters of the prototype are changed. This is done as an important assessment of the craft as an autonomous drone as the craft may be used for sea mapping purposes in which energy usage efficiency is essential. Multiple control algorithms are considered, classic PID as well as linear quadratic methods and later on used and tested through simulation in Simscape Multibody as means of verification. Further strategies on motion control are developed to increase stability and robustness by extending the amount of controllable variables. Results show that the coupling effects are minimal when the system is disturbed and suggests that the rather simplified control design is feasible, this however can only be said when moving about the equilibrium point as a linearization is done. Concerning scaling effects the craft needs a faster response of control that puts higher requirements on hardware when scaled down. For example with relatively slow servos to actuate the system, it exhibits oscillatory behavior. Also measurement noise is amplified to a higher extend which may cause unwanted behavior. i Acknowledgements I would like to thank the team over at the Maritime Robotics Lab and especially the one working with the FoilCart-project, Ivan Stenius, Nicholas Honeth, An- ton Svensson and Fredrik Löfblom for providing me with more insights into naval architecture and a better understanding of the project. I would also like to thank my supervisor Binbin Lian for all the help and discussions concern- ing difficulties and solutions as well as my examiner Lei Feng for interesting viewpoints and questions. Contents 1 Introduction 1 1.1 Background . .1 1.2 Problem definition . .4 1.3 Purpose . .4 1.4 Research question . .5 1.5 Research methodology & Scope . .5 1.6 Ethical considerations . .6 2 FoilCart Dynamics & Modelling 7 2.1 The FoilCart . .7 2.2 The Inverted Pendulum . .8 2.2.1 Broom on a cart . .8 2.2.2 Spherical pendulum on a cart . .8 2.2.3 Lagrangian mechanics . 10 2.2.4 Linearization & Decoupling . 13 2.2.5 FoilCart actuation and dynamics . 14 2.3 Wing dynamics . 16 3 Control Design 19 3.1 The plant model . 19 3.1.1 Equations of motion . 19 3.2 Control algorithms . 20 3.2.1 PID . 21 3.2.2 LQ . 21 3.3 Controller choice . 26 3.4 State space representation . 30 3.4.1 Controllability . 31 3.5 Cascaded control . 32 ii CONTENTS iii 4 Simulation verification 35 4.1 Simulink modelling . 35 4.1.1 Disturbance modelling . 37 4.2 Test cases . 39 4.2.1 Case 1 . 40 4.2.2 Case 2 . 42 4.2.3 Case 3 . 44 4.3 System Scaling . 46 4.3.1 Parameters . 46 5 Results 48 5.1 Cases . 49 5.1.1 Case 1 . 49 5.1.2 Case 2 . 54 5.1.3 Case 3 . 63 5.1.4 Result analysis . 68 5.2 Closed loop placement . 69 5.3 Sensitivity & Complementary Sensitivity . 70 6 Conclusion & future work 73 6.1 Conclusion . 73 6.2 Future work . 74 Bibliography 76 List of Figures 1.1 Examples of types of existing hydrofoils. [3] . .2 1.2 Bell’s prototype hydrofoil-boat HD-4 in 1919. [5] . .2 1.3 Prototype design of the FoilCart project at MRL. .4 2.1 Figure demonstrating the broom-on-a-cart dynamics. .8 2.2 Figure demonstrating the broom-on-a-cart dynamics on a plane.9 2.3 Figure depicting the simplified actuation in the roll plane of the FoilCart. 14 2.4 Figure depicting the simplified actuation in the pitch plane of the FoilCart. 15 2.5 A comparison between MATLABs linearization tool for Simulink models and the derived mathematically model, the figure is a pole-zero mapping of the eigenvalues of the state space matrix. 16 2.6 Figure depicting some of the dynamics acting upon a moving wing profile. 16 2.7 Figure showing the profile of a NACA0015-wing. 17 2.8 Figure showing the varying lift/drag parameter with respect to angle of attack. 18 3.1 Figure showing an example of an LQI setup. 23 3.2 Figure showing an example of the sensitivity function compared between LQI and LQR. 24 3.3 MATLAB’s application PID-tuner which is used to find a suit- able controller for the plant. 26 3.4 A comparison between an LQR controller and the PID designed in previous figure. 27 3.5 MATLAB’s application PID-tuner which is used to find a suit- able controller for the plant. 28 3.6 A comparison on sensitivity between an LQR controller and the PID with changed parameters. 29 iv LIST OF FIGURES v 3.7 Figure displaying the suggested cascaded setup for control. 32 3.8 Figure displaying MATLAB’s application PID-tuner........ 34 4.1 Figure showing a simplified FoilCart model designed in Simulink (Simscape Multibody). 35 4.2 Figure showing the controller setup designed in Simulink. 36 4.3 Figure showing the Simscape Multibody setup for the model. 37 4.4 Figure showing the Simscape model with the suggested distur- bance model. 38 4.5 Figure showing the Simscape Multibody setup for the model in a simplified version for Case 1. 40 4.6 Figure showing the forces acting on the simplified version of the model. 41 4.7 Figure showing the controller setup designed in Simulink. 41 4.8 Figure showing the more advanced version of the Simscape model. 42 4.9 Servo step response, it takes approximately 100 ms for the servo to reach it’s target. 43 4.10 Figure showing the thrust controller in the Simulink model. 44 4.11 Figure showing the setup of the controller with auto-tuned PID blocks for a 5-DOF system. 45 4.12 Figure showing the Simulink setup for enhancing the actuator angles.